Mogakolodi Ngele, who started from the bench against Stellenbosch FC last Sunday, earned a start along with Thobani Mncwango and Tshwarelo Bereng.
Leopards wasted no time to going ahead as Ngele rewarded their interim coach Alan Clark for the start with the opener inside seven minutes.
North West University remained under increasing pressure towards the 20th minute, while Ngele threatened a brace though Ramadivhane pulled off a double save to deny the winger.
The visitors looked to get back into the clash following the half-hour mark, but Leopards goalkeeper Jonas Mendes in the home side's goal proved difficult to breach.
Mncwango should've added more to Lidoda Duvha's tally in added time but blazed over the top from the penalty circle.
A forced changed 52 minutes in the second half saw Mendes making way for Rotshidza Muleka between the sticks after struggling with injury.
Lidoda Duvha however still doubled their advantage six minutes later when Mncwango got the better of the defence to head past Ramadivhane.
Alan Clark put on a second change for the hosts 77 minutes in, as Bereng made way for Thabiso Mokoena.
Leopards secured their third in the last nine minutes when Mncwango completed his brace after tapping home Lesedi Kapinga's rebound.
Meanwhile, Tumelo Khutlang, who replaced Ngele minutes earlier, gave Lidoda Duvha a fourth goal deep in added time to seal their spot in the last 16.